Favard operator
Functional analysis operator
From Wikipedia, the free encyclopedia
In functional analysis, a branch of mathematics, the Favard operators are defined by:
={\frac {1}{\sqrt {n\pi }}}\sum _{k=-\infty }^{\infty }{\exp {\left({-n{\left({{\frac {k}{n}}-x}\right)}^{2}}\right)}f\left({\frac {k}{n}}\right)}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/acaa954568b1a95634863d8ed6f72b1bcf19530f)
where , . They are named after Jean Favard.
Functional analysis operator
From Wikipedia, the free encyclopedia
In functional analysis, a branch of mathematics, the Favard operators are defined by:
where , . They are named after Jean Favard.
={\frac {1}{n\gamma _{n}{\sqrt {2\pi }}}}\sum _{k=-\infty }^{\infty }{\exp {\left({{\frac {-1}{2\gamma _{n}^{2}}}{\left({{\frac {k}{n}}-x}\right)}^{2}}\right)}f\left({\frac {k}{n}}\right)}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/10d087da78a01d791b95404b1905104f7f161f19)
